まきこむ
to roll up, to involve
The scroll rolls up and whatever was lying beside it goes in with it. The same mac まき as 捲る and the same come こむ as 込める. Your friend was standing too close: まきこむ.
関わる かかわる is being connected to a thing. 巻き込む is dragging somebody else into it with you.
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Emaki is not affiliated with, or endorsed by, Kaishi 1.5k or its authors. The word, reading and meaning come from the Kaishi 1.5k deck, used with their permission. The mnemonic, the note and the kanji breakdown are original work, published under CC BY-SA 4.0.